Design of Sampled-Data High-Gain PD Control Systems

Abstract

Proportional and derivative (PD)control is a simple and effective control technique for a wide class of dynamic systems. System uncertainties due to nonlinearity distortions, parameter variations, or external disturbances can be suppressed by increasing the feedback gains. In practice, however, there are limits to the PD gains without causing instability. The instability is usually attributed to measurement noise or high-frequency unmodeled dynamics excited by the high feedback gains. In this paper we show that the sample-and-hold effect in a digital control system may cause instability in an otherwise stable PD control system. With proper approximations, explicit and practical stability criteria are derived relating the magnitudes of the feedback gains to the sampling period and other system parameters. Basides the sampling period, the stability of the closed-loop system is also significantly affected by the computation time, which is often neglected in theoretical analyses or numerical simulations. Case studies are presented to illustrate the use of the stability criteria in the design of high-gain PD control systems.